In this work, we have proposed augmented KRnets including both discrete and continuous models. One difficulty in flow-based generative modeling is to maintain the invertibility of the transport map, which is often a trade-off between effectiveness and robustness. The exact invertibility has been achieved in the real NVP using a specific pattern to exchange information between two separated groups of dimensions. KRnet has been developed to enhance the information exchange among data dimensions by incorporating the Knothe-Rosenblatt rearrangement into the structure of the transport map. Due to the maintenance of exact invertibility, a full nonlinear update of all data dimensions needs three iterations in KRnet. To alleviate this issue, we will add augmented dimensions that act as a channel for communications among the data dimensions. In the augmented KRnet, a fully nonlinear update is achieved in two iterations. We also show that the augmented KRnet can be reformulated as the discretization of a neural ODE, where the exact invertibility is kept such that the adjoint method can be formulated with respect to the discretized ODE to obtain the exact gradient. Numerical experiments have been implemented to demonstrate the effectiveness of our models.
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Variational approximation, such as mean-field (MF) and tree-reweighted (TRW), provide a computationally efficient approximation of the log-partition function for a generic graphical model. TRW provably provides an upper bound, but the approximation ratio is generally not quantified. As the primary contribution of this work, we provide an approach to quantify the approximation ratio through the property of the underlying graph structure. Specifically, we argue that (a variant of) TRW produces an estimate that is within factor $\frac{1}{\sqrt{\kappa(G)}}$ of the true log-partition function for any discrete pairwise graphical model over graph $G$, where $\kappa(G) \in (0,1]$ captures how far $G$ is from tree structure with $\kappa(G) = 1$ for trees and $2/N$ for the complete graph over $N$ vertices. As a consequence, the approximation ratio is $1$ for trees, $\sqrt{(d+1)/2}$ for any graph with maximum average degree $d$, and $\stackrel{\beta\to\infty}{\approx} 1+1/(2\beta)$ for graphs with girth (shortest cycle) at least $\beta \log N$. In general, $\kappa(G)$ is the solution of a max-min problem associated with $G$ that can be evaluated in polynomial time for any graph. Using samples from the uniform distribution over the spanning trees of G, we provide a near linear-time variant that achieves an approximation ratio equal to the inverse of square-root of minimal (across edges) effective resistance of the graph. We connect our results to the graph partition-based approximation method and thus provide a unified perspective. Keywords: variational inference, log-partition function, spanning tree polytope, minimum effective resistance, min-max spanning tree, local inference
Time-to-event endpoints show an increasing popularity in phase II cancer trials. The standard statistical tool for such endpoints in one-armed trials is the one-sample log-rank test. It is widely known, that the asymptotic providing the correctness of this test does not come into effect to full extent for small sample sizes. There have already been some attempts to solve this problem. While some do not allow easy power and sample size calculations, others lack a clear theoretical motivation and require further considerations. The problem itself can partly be attributed to the dependence of the compensated counting process and its variance estimator. We provide a framework in which the variance estimator can be flexibly adopted to the present situation while maintaining its asymptotical properties. We exemplarily suggest a variance estimator which is uncorrelated to the compensated counting process. Furthermore, we provide sample size and power calculations for any approach fitting into our framework. Finally, we compare several methods via simulation studies and the hypothetical setup of a Phase II trial based on real world data.
Ageing of lithium-ion batteries results in irreversible reduction in performance. Intrinsic variability between cells, caused by manufacturing differences, occurs throughout life and increases with age. Researchers need to know the minimum number of cells they should test to give an accurate representation of population variability, since testing many cells is expensive. In this paper, empirical capacity versus time ageing models were fitted to various degradation datasets for commercially available cells assuming the model parameters could be drawn from a larger population distribution. Using a hierarchical Bayesian approach, we estimated the number of cells required to be tested. Depending on the complexity, ageing models with 1, 2 or 3 parameters respectively required data from at least 9, 11 or 13 cells for a consistent fit. This implies researchers will need to test at least these numbers of cells at each test point in their experiment to capture manufacturing variability.
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of weighted graphs and retains many of its intuitive and desired properties. Interestingly, we find that a number of famous concepts in graph theory and network science can be reinterpreted in this setting as variances and covariances of particular distributions. As a particular application, we define the maximum variance problem on graphs with respect to the effective resistance distance, and characterize the solutions to this problem both numerically and theoretically. We show how the maximum variance distribution is concentrated on the boundary of the graph, and illustrate this in the case of random geometric graphs. Our theoretical results are supported by a number of experiments on a network of mathematical concepts, where we use the variance and covariance as analytical tools to study the (co-)occurrence of concepts in scientific papers with respect to the (network) relations between these concepts.
The data processing inequality is the most basic requirement for any meaningful measure of information. It essentially states that distinguishability measures between states decrease if we apply a quantum channel and is the centerpiece of many results in information theory. Moreover, it justifies the operational interpretation of most entropic quantities. In this work, we revisit the notion of contraction coefficients of quantum channels, which provide sharper and specialized versions of the data processing inequality. A concept closely related to data processing is partial orders on quantum channels. First, we discuss several quantum extensions of the well-known less noisy ordering and relate them to contraction coefficients. We further define approximate versions of the partial orders and show how they can give strengthened and conceptually simple proofs of several results on approximating capacities. Moreover, we investigate the relation to other partial orders in the literature and their properties, particularly with regards to tensorization. We then examine the relation between contraction coefficients with other properties of quantum channels such as hypercontractivity. Next, we extend the framework of contraction coefficients to general f-divergences and prove several structural results. Finally, we consider two important classes of quantum channels, namely Weyl-covariant and bosonic Gaussian channels. For those, we determine new contraction coefficients and relations for various partial orders.
In this paper, we introduce a new framework for unsupervised deep homography estimation. Our contributions are 3 folds. First, unlike previous methods that regress 4 offsets for a homography, we propose a homography flow representation, which can be estimated by a weighted sum of 8 pre-defined homography flow bases. Second, considering a homography contains 8 Degree-of-Freedoms (DOFs) that is much less than the rank of the network features, we propose a Low Rank Representation (LRR) block that reduces the feature rank, so that features corresponding to the dominant motions are retained while others are rejected. Last, we propose a Feature Identity Loss (FIL) to enforce the learned image feature warp-equivariant, meaning that the result should be identical if the order of warp operation and feature extraction is swapped. With this constraint, the unsupervised optimization is achieved more effectively and more stable features are learned. Extensive experiments are conducted to demonstrate the effectiveness of all the newly proposed components, and results show that our approach outperforms the state-of-the-art on the homography benchmark datasets both qualitatively and quantitatively. Code is available at //github.com/megvii-research/BasesHomo.
The DeepFakes, which are the facial manipulation techniques, is the emerging threat to digital society. Various DeepFake detection methods and datasets are proposed for detecting such data, especially for face-swapping. However, recent researches less consider facial animation, which is also important in the DeepFake attack side. It tries to animate a face image with actions provided by a driving video, which also leads to a concern about the security of recent payment systems that reply on liveness detection to authenticate real users via recognising a sequence of user facial actions. However, our experiments show that the existed datasets are not sufficient to develop reliable detection methods. While the current liveness detector cannot defend such videos as the attack. As a response, we propose a new human face animation dataset, called DeepFake MNIST+, generated by a SOTA image animation generator. It includes 10,000 facial animation videos in ten different actions, which can spoof the recent liveness detectors. A baseline detection method and a comprehensive analysis of the method is also included in this paper. In addition, we analyze the proposed dataset's properties and reveal the difficulty and importance of detecting animation datasets under different types of motion and compression quality.
Constructing probability densities for inference in high-dimensional spectral data is often intractable. In this work, we use normalizing flows on structured spectral latent spaces to estimate such densities, enabling downstream inference tasks. In addition, we evaluate a method for uncertainty quantification when predicting unobserved state vectors associated with each spectrum. We demonstrate the capability of this approach on laser-induced breakdown spectroscopy data collected by the ChemCam instrument on the Mars rover Curiosity. Using our approach, we are able to generate realistic spectral samples and to accurately predict state vectors with associated well-calibrated uncertainties. We anticipate that this methodology will enable efficient probabilistic modeling of spectral data, leading to potential advances in several areas, including out-of-distribution detection and sensitivity analysis.
In the era of big data, people face enormous challenges in acquiring information and knowledge. A knowledge graph (KG) lays the foundation for the knowledge-based organization and intelligent application in the Internet age with its powerful semantic processing capabilities and open organization capabilities. In recent years, the research and applications of large-scale knowledge graph libraries have attracted increasing attention in academic and industrial circles. The knowledge graph aims to describe the various entities or concepts and their relationships existing in the objective world, which constitutes a huge semantic network map. It usually stores knowledge in the form of triples (head entity, relationship, tail entity), which can be simplified to $(h, r, t)$.
Various 3D reconstruction methods have enabled civil engineers to detect damage on a road surface. To achieve the millimetre accuracy required for road condition assessment, a disparity map with subpixel resolution needs to be used. However, none of the existing stereo matching algorithms are specially suitable for the reconstruction of the road surface. Hence in this paper, we propose a novel dense subpixel disparity estimation algorithm with high computational efficiency and robustness. This is achieved by first transforming the perspective view of the target frame into the reference view, which not only increases the accuracy of the block matching for the road surface but also improves the processing speed. The disparities are then estimated iteratively using our previously published algorithm where the search range is propagated from three estimated neighbouring disparities. Since the search range is obtained from the previous iteration, errors may occur when the propagated search range is not sufficient. Therefore, a correlation maxima verification is performed to rectify this issue, and the subpixel resolution is achieved by conducting a parabola interpolation enhancement. Furthermore, a novel disparity global refinement approach developed from the Markov Random Fields and Fast Bilateral Stereo is introduced to further improve the accuracy of the estimated disparity map, where disparities are updated iteratively by minimising the energy function that is related to their interpolated correlation polynomials. The algorithm is implemented in C language with a near real-time performance. The experimental results illustrate that the absolute error of the reconstruction varies from 0.1 mm to 3 mm.
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